Increasingly, space systems and proposed space systems require satellite constellations, i.e., arrays of at least two satellites, to achieve system objectives. Constellations are necessary to provide the desired global coverage for many communication, remote sensing and scientific applications. Some systems in development will utilize hundreds and even thousands of satellites to achieve the desired coverage. Typically, the individual satellites in these constellations will employ inclined near-circular orbits to enhance coverage of areas distant from the equatorial plane. In addition, some proposed systems may employ relatively low altitude orbits, for example, in the case of cellular communications systems, to facilitate signal transmittal.
To ensure that the constellation provides the desired global coverage, the satellites must maintain their assigned stations in the constellation. It is desirable, particularly in constellations of large numbers of satellites, that this "formationkeeping" be achieved autonomously thereby simplifying system control. For example, autonomous formationkeeping could be achieved if each satellite was capable of sensing deviations from its assigned station and automatically implemented corrective maneuvers.
Internal direct approaches to autonomous constellation formationkeeping that have been suggested involve monitoring intersatellite spacing, differential orbital elements, or a combination thereof. According to such internal approaches, satellites would exchange position, rate of position, element set information, or a combination thereof on a continuous basis. Each satellite would then employ an algorithm, based on intersatellite spacing or element information, to determine differential station or element errors and implement corrective maneuvers as required to restore the desired spacing. In large systems, the constellation could be divided into rings, each comprising a number of satellites in substantially coplanar orbits, with each satellite determining its position relative to a ring leader satellite which would in turn key off leader satellites in adjacent rings. Thus, if a fixed geometry constellation was desired, formationkeeping according to the internal approach would cause the satellites in each ring to attempt convergence to neighboring satellite values of inclination, ascending node, argument of perigee, semi-major axis, and eccentricity. In addition, formationkeeping in such a system would require maintenance of constant interring spacing as well as constant distances and bearing angles with respect to satellites in adjacent rings.
There are a number of problems associated with an internal approach, particularly when high inclination and low altitude orbits are employed. First, orbital perturbation makes it difficult to identify station errors from systematic intersatellite spacing variation. Direct algorithms, which rely in part on differential element sets, must deal with poorly defined parameters of eccentricity and argument of perigee. At the least, both parameters will fluctuate rapidly due to both deliberate thrusting and the effects of orbital perturbations. The effects of minute thrusts on orbital elements can not be measured immediately but are revealed only through displacements observed a sizeable fraction of an orbit revolution later. The perturbative forces exerted on each satellite in the constellation include the following. The high order geopotential distortion due to Earth oblateness induces a bulk rotation, or precession of all orbit nodes with respect to inertial space. Lower order variations of the geopotential vary with location so as to induce undulating variations in altitude, intrack, and out of track positions about a single orbit. In addition, each satellite will be subjected to a variable component of drag. Drag accelerations vary due to factors such as satellite altitude variations due to the oblateness of the Earth add its atmosphere, localized variation in exospheric temperature associated with solar intensity, day to night and seasonal variations in atmospheric thickness, hourly and geographical variations due to change in geomagnetic index, and satellite to satellite variation in satellite profile and mass. Other perturbing forces important for higher altitude constellations include the gravitational pull of third bodies, such as the moon and sun, and forces induced by solar radiation pressure. Further variations in intersatellite spacing would result from orbital eccentricity residuals. Due to the spatial and temporal variability of these perturbing forces and effects, each satellite will experience a unique perturbation history and trace a unique orbital path. Consequently, identifying station errors from variations in intersatellite spacing would be extremely difficult.
Another problem associated with the internal approach to formationkeeping is the difficulty of calculating appropriate corrective maneuvers. After identifying station errors from systematic variations in intersatellite spacing, it would be necessary to implement a corrective maneuver to restore the desired spacing relative to satellites which may themselves be maneuvering. However, algorithms to implement the corrective maneuvers would need to address such things as complex drift patterns and circuitous trajectories (a approximately described by the Clohessy-Wiltshire equations) associated with maneuvering relative to rotating coordinate frames. The algorithms would have to allow for perturbative variations along the transfer trajectory plus the maneuver plans and projected perturbations of adjacent satellites. The identification of suitable combinations of thrust, thrust directions, plus start and stop times will present an extremely formidable challenge to designers using the direct method. Much fuel could be wasted on unnecessary backtracking due to the extreme complexity and required timing and precision of maneuvers. Thus, implementing corrective maneuvers would involve intensive processing.
Yet another problem associated with the internal approach to formationkeeping is the potential for error accumulation when station errors are determined relative to variable internal constellation geometry. If a first satellite engages in corrective maneuvering responsive to intersatellite spacing variation relative to a second satellite which itself is out of station, formationkeeping problems could be compounded to the extent of a chain reaction disruption of the entire constellation. Thus, unless a system was devised to correct formationkeeping errors relative to coordinates independent of constellation geometry, relative position errors could accumulate resulting, for example, in a build-up of constellation eccentricity plus secular changes in altitude and inclination.